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 A202472 Goldbach's Problem extended to subtraction: number of decompositions of 2n into unordered differences of two primes, p, q, where p < 2n < q. 4

%I #18 Jan 03 2016 16:35:30

%S 0,1,1,2,2,3,2,3,3,3,2,6,4,3,6,3,4,6,4,5,8,4,4,7,6,4,9,8,4,11,5,5,11,

%T 6,8,9,4,7,11,7,4,13,7,5,15,7,8,13,8,9,11,7,7,13,10,5,13,7,7,19,9,8,

%U 17,9,10,16,9,9,15,12,7,19,9,7,19,9,12,17,8,14

%N Goldbach's Problem extended to subtraction: number of decompositions of 2n into unordered differences of two primes, p, q, where p < 2n < q.

%H T. D. Noe, <a href="/A202472/b202472.txt">Table of n, a(n) for n = 1..10000</a>

%t Table[Length[Select[Prime[Range[PrimePi[2*n]]], PrimeQ[2*n + #] &]], {n, 100}] (* _T. D. Noe_, Apr 16 2013 *)

%o (PARI) a(n)=my(s);forprime(p=2,2*n,s+=isprime(2*n+p));s \\ _Charles R Greathouse IV_, Dec 19 2011

%o (C++)

%o #include <iostream>

%o using namespace std;

%o int main()

%o { int p[25] = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97};

%o int count, istart = 2;

%o for(int n=1; n<=25; n++)

%o {

%o if(2*n>p[istart]) istart++;

%o count = 0;

%o for(int j=1; p[j]<2*n; j++)

%o for(int i=istart; p[i]-p[j]<=2*n; i++)

%o if(p[i]-p[j]==2*n) count++;

%o cout << n << ". " << count << endl;

%o }

%o return 0;

%o } // code for the first 25 integers, _James D. Klein_, Dec 21 2011

%Y Extension of A002375.

%K nonn

%O 1,4

%A _James D. Klein_, Dec 19 2011

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Last modified October 2 22:30 EDT 2023. Contains 365841 sequences. (Running on oeis4.)